I believe it was filmed unlike some of the other music variety shows of the 60s that also aired in prime time.
Even if it's not and the film elements don't exist in ABC's vault, the King Family has the complete run on tape for both incarnations of the program (Not limited to just the holiday specials that were routinely reaired each holiday season into the 1990s, and the non holiday episodes which even saw some syndication in the 70s). It's not a lost program, just send one of the family members a email for a confirmation. :)
They put up a new song on YouTube every few months. There are some excellent ones with the King Cousins especially that they've uploaded. They were always the highlights of the program if you ask me. They also sell several episodes from the series on DVD (With hopefully more to come, I'd love to see them make the entire run available).
Here are some of my favorites that they've uploaded:
http://www.youtube.com/watch?v=WXFLN2z_If4
http://www.youtube.com/watch?v=a116Y8qXiQQ
http://www.youtube.com/watch?v=dPsx2FXji0k
http://www.youtube.com/watch?v=1HUW32iTX3k
Quote:
Originally Posted by
Neil Brock 
Are you talking about the ABC show from the mid-60s? If so, I really question as to the show still existing. They aren't at any archive that I'm aware of and ABC was notorious for dumping all of their videotaped variety shows of that era. I think if it did exist on kinescopes, then they would be at UCLA but they are not.